Model order reduction for temperature-dependent nonlinear mechanical systems: A multiple scales approach

Jain, Shobhit; Tiso, Paolo

doi:10.1016/j.jsv.2019.115022

Cited by 16 publications

(7 citation statements)

References 24 publications

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“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [68,138,250], piezoelectric material nonlinearities [62,139,299], non-local models for nanostructures [238,239], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,267] with applications to blades [79,224,226,271], large strain elastic nonlinear constitutive laws [187], fluid-structure interaction [107,165] and coupling with nonlinear aeroelastic forces [48]; or thermal effects [99,219], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization, could be also used with such tools [65,291,308,309].…”

Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

2021

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This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures dis-C. Touzé (B)

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Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

2021

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“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [66,137,251], piezoelectric material nonlinearities [60,138,299], non-local models for nanostructures [239,240], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,268] with applications to blades [77,225,227,272], large strain elastic nonlinear constitutive laws [188], fluid-structure interaction [105,166] and coupling with nonlinear aeroelastic forces [46]; or thermal effects [97,220], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization could be also used with such tools [63,292,308,309].…”

Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Touzé,

Vizzaccaro,

Thomas

2021

Preprint

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This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes (NNMs) and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations (PDE). They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then the specific case of structures discretized with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models (ROMs) relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.

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“…23 A powerful trait of such approaches is their suitability for both linear 24,25 and nonlinear applications 26,27 for a broad array of tasks, including design optimisation [28][29][30] or multi-scale analysis. 31,32 When exploring SHM applications involving fracture mechanics problems, where localised damage features are involved, ROMs have been reported to balance accelerated model evaluations with precision, thus offering an attractive framework for problems of condition assessment or damage localisation. 33,34 For example, POD-based reduction has been employed to address multi-scale 35 or inter-layer models of failure, 36,37 whereas a number of references have proposed basis enrichment techniques that refine the projection basis in an adaptive manner during the online analysis, either via Krylov subspaces 38 or by evaluating the response in regions with localised features of interest in a full-order dimension when needed.…”

Section: Introductionmentioning

confidence: 99%

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Agathos,

Vlachas,

Garland

et al. 2024

Numerical Meth Engineering

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In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection‐based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low‐dimensional spaces, in which solutions are represented. In the proposed approach, low‐dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

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Model order reduction for temperature-dependent nonlinear mechanical systems: A multiple scales approach

Cited by 16 publications

References 24 publications

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

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